Aircraft: B737
Phase of flight: Climb
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR; Flight Deck / Cabin / Aircraft Event Illness / Injury; Inflight Event / Encounter Weather / Turbulence

We had flown in on the all-nighter ZZZ-ZZZ1 and arrived at XA:00L; about 30 minutes late. By the time we finally got to the hotel it was around XB:00L. Pickup was at XL:30L and once we arrived at the airport it was discovered that the aircraft was late inbound and on top of that; the gate was occupied by a delayed flight. The end result was that we could not get onto our aircraft until it was almost scheduled departure time. We were then further delayed due to the ramp shutting down because of thunderstorms which had rolled through. It looked like we were finally ready to go so; as the PF; I gave the Captain's Departure brief and the Pilot Flying brief. This was immediately followed by the Preflight checklist. Unfortunately we were then further delayed another 20 minutes for connecting bags. By the time we blocked out we were 1:17 behind schedule. We conducted a single engine taxi; starting the second engine approaching runway. All appropriate checklists were run and flight was given clearance to 'line up and wait'. Upon receipt of takeoff clearance I pushed the throttles up and the pushed the TOGA button. The auto-throttles set takeoff thrust and I made the 'check thrust' callout. The PM announced that thrust was set at 95.7% which was the expected number per the takeoff data message. However; thrust continued to advance and finally settled at 98.2% which was the value displayed in the FMC. PM subsequently announced 'thrust set; 98.2%'. I remember thinking to myself that the power setting felt pretty high; but it matched the displayed N1 setting in the FMC so I suppressed my concerns. Obviously in hindsight I realize that one possible explanation for the higher than expected thrust was that the engine bleed air switch was positioned to off. We took off and cleaned up the aircraft then ran the After Takeoff checklist. Climbing via the SID our initial altitude was 10;000; but we were subsequently given a climb to 17;000 FT. Passing through approximately 11;000 FT the Cabin Altitude warning horn began to blare and the Cabin Altitude warning light illuminated. We conducted the immediate action items for Cabin Altitude Warning Horn/Light in Flight. I selected ALT HLD to level the aircraft and attempted to select A/P A; which would not select. I continued to hand fly the aircraft and established communication with ATC; and requesting an immediate descent to 9000 FT. I directed the FO to run the QRH FOR Cabin Altitude Warning Horn/Light in Flight. In the heat of the battle; with everything happening; the FAs repeatedly chimed the cockpit out of concern for our safety. From their jump seat they clearly heard the warning horn and did not know what was going on. Not having time at that moment to talk with them I made a PA announcement for the FAs to be seated; which allayed their fears of our demise and got them to cease chiming us. While running the QRH the FO realized that the engine bleed air switches were in the 'off' position. The FO turned the switches to the 'on' position and cabin pressurization was then re-established in the manual mode. This; combined with the descent; resulted in the silencing of the warning horn and the extinguishing of the warning light. We removed our oxygen masks and then got about the task of coordinating a return to ZZZ1. Switching roles; I handed the aircraft to the FO who was subsequently able to engage the B autopilot. ATC gave us vectors direct to ZZZ1; but since we were not ready for the approach we requested delaying vectors/holding while we went about the task of coordination with company. I sent a message to dispatch to 'call me' and seconds later communication was established. Maintenance Control and Dispatch were conferenced in and we discussed what had happened; including the fact that we were in manual pressurization having been unable to establish pressurization using the Auto mode. All things having been considered I chose to return to ZZZ1. As we were 10;000 pounds overweight for landing; the next decision to be made was whether to burn down our fuel or land overweight. Discussion with Maintenance Control gave me the sense that an overweight landing was really a nonissue as long as it was not a hard landing. So given the choice between burning down to landing weight - about two hours - or landing overweight I chose the latter. This decision was influenced by the fact that the FAs had reported that several passengers were feeling ill.Given the higher approach speeds associated with the heavy weight; we decided to request vectors to the longest runway - 27R. ATC gave us vectors for the ILS approach to 27R and as we proceeded inbound we completed the Approach Descent followed by the Approach checklist. The approach and landing were normal with a smooth touchdown. After clearing the runway we informed tower that no further assistance was required. When we taxied to the gate we noticed that the aircraft was still pressurized so I instructed the FO to open the outflow valve using the manual control switch. The aircraft was depressurized; the jetway pulled up and the passengers disembarked. Even though we could legally have continued on with the flight; with all that had happened we elected not to consider this but rather to terminate. Notes: The Cabin Altitude Warning Horn/Light In Flight QRH has a serious shortcoming. The checklist ends with the establishment of cabin pressurization in the manual mode. No mention is made of system degradation or future required actions; such as depressurizing the aircraft prior to landing. Other checklist; such as the Auto Fail QRH; all end with 'Checklist complete except deferred items'; one of which is how and when to depressurize the aircraft for landing when in manual mode. With no guidance; reminders or mention of this in the Cabin Altitude Warning Horn/Light in Flight QRH; the thought of depressurizing the aircraft never crossed my mind as this is always taken care automatically by the pressurization system. Unfortunately we were in the manual mode and ended up landing with the cabin pressurized. After the fact I realize there is a Supplementary 'Manual Mode Operation' QRH which would have been a good reference item for the Cabin Altitude Warning Horn/Light in Flight QRH. The FO states that she never touched the engine bleed air switches during preflight; taxi and takeoff; so they must have been off when we got to the aircraft. There is no checklist or parking/termination procedure that puts these switches in this position. Consequently; I believe habit lead her to assume that these switches were in the correct position -ON - when in fact were actually OFF. When I responded to the challenge on the Preflight Checklist challenge 'Pressurization'; saw that the pressurization control panel had the correct altitudes set; auto was selected and bleed/pack switches were married up; leading me to assume they were set to the correct position. Again; this is because Bleeds - OFF is such an unusual position my brain registered that they were both ON. B737 Captain reported receiving a cabin altitude warning horn and light. They soon realized the engine bleed switches were in the off position. Reporter mentioned engine bleed switch position is not on their checklist.